Cremona's table of elliptic curves

17472 = 2⁶ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	17472cm	Isogeny class
Conductor	17472	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	465174528 = 217 · 3 · 7 · 132	Discriminant
Eigenvalues	2- 3-  2 7+ -4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-605697,181237503]	[a1,a2,a3,a4,a6]
Generators	[600094:91005:1331]	Generators of the group modulo torsion
j	187491149065688834/3549	j-invariant
L	6.3930278477561	L(r)(E,1)/r!
Ω	0.86063015669614	Real period
R	7.4283102887054	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17472h5 4368d5 52416et6 122304gh6	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472cm5

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	2	+	-4	+	2	-4	0	2	0	2	-6	4	8	10	-4	2	-4	0	2	-8	-12	-6	10

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Quadratic twists for elliptic curve 17472cm5

-4	8	-3	-7
17472h5	4368d5	52416et6	122304gh6

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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